Algorithm writing tips?

 The new algorithm

Code:

import java.util.*;

public class Project60 {

    //Find a set of five primes for which any two primes concatenate to produce another
    //prime.
    
    private static Hashtable<Long, Boolean> primesRecall = new Hashtable<Long, Boolean>();
    private static ArrayList<Long> primesList = new ArrayList<Long>();
    
    public static void main(String[] args){
        double time = System.currentTimeMillis();
        primesList.add(3L);
        primesList.add(7L);
        long nxtPrime = 11L;
        int digitLimit = 4;
        
        while(true){
            
            //Fills the primesList ArrayList.
            while(nxtPrime <= Math.pow(10, digitLimit)){
                if(isPrime(nxtPrime)){
                    primesList.add(nxtPrime);
                    primesRecall.put(nxtPrime, true);
                }
                nxtPrime += 2;
                if(isPrime(nxtPrime)){
                    primesList.add(nxtPrime);
                    primesRecall.put(nxtPrime, true);
                }
                nxtPrime += 4;
            }
            while(true){
                if(isPrime(nxtPrime)){
                    primesList.add(nxtPrime);
                    primesRecall.put(nxtPrime, true);
                    break;
                }
                nxtPrime += 2;
                if(isPrime(nxtPrime)){
                    primesList.add(nxtPrime);
                    primesRecall.put(nxtPrime, true);
                    break;
                }
                nxtPrime += 4;
            }
            
            time = System.currentTimeMillis() - time;
            time /= 60000;
            System.out.println("Step 1 Time: " + time + " minutes.");
            time = System.currentTimeMillis();
            
            //Fill a complete primesTable of what primes concatenate with other primes
            //to produce new primes, in preparation for the next step.
            int size = primesList.size();
            boolean[][] primesTable = new boolean[size][size];
            long prime1 = 0;
            for(int i = 0; i < size - 1; i++){
                prime1 = primesList.get(i);
                long prime2 = 0;
                for(int j = 0; j < size - 1; j++){
                    prime2 = primesList.get(j);
                    long result1 = 0;
                    long result2 = 0;
                    for(int k = 1; result1*result2 == 0; k++){
                        long power = (long)Math.pow(10, k);
                        if(power > prime2 && result1 == 0)
                            result1 = prime1 * power + prime2;
                        if(power > prime1 && result2 == 0)
                            result2 = prime2 * power + prime1;
                    }
                    if((isPrime(result1)) &&
                            (isPrime(result2))){
                        primesTable[i][j] = true;
                        primesTable[j][i] = true;
                    }
                }
            }
            
            time = System.currentTimeMillis() - time;
            time /= 60000;
            System.out.println("Step 2 Time: " + time + " minutes.");
            time = System.currentTimeMillis();
            
            //Attempt to find the set of five primes, if it exists.
            for(int i1 = 0; i1 < size; i1++){
                for(int i2 = 0; i2 < size; i2++){
                    for(int i3 = 0; i3 < size &&
                            primesTable[i1][i2]; i3++){
                        for(int i4 = 0; i4 < size &&
                                primesTable[i1][i3] &&
                                primesTable[i2][i3]; i4++){
                            for(int i5 = 0; i5 < size &&
                                    primesTable[i1][i4] &&
                                    primesTable[i2][i4] &&
                                    primesTable[i3][i4]; i5++){
                                if(primesTable[i1][i5] &&
                                        primesTable[i2][i5] &&
                                        primesTable[i3][i5] &&
                                        primesTable[i4][i5]){
                                    System.out.println(primesList.get(i1));
                                    System.out.println(primesList.get(i2));
                                    System.out.println(primesList.get(i3));
                                    System.out.println(primesList.get(i4));
                                    System.out.println(primesList.get(i5));
                                    System.out.println("Sum: " + (primesList.get(i1) +
                                            primesList.get(i2) + primesList.get(i3) +
                                            primesList.get(i4) + primesList.get(i5)));
                                
                                    time = System.currentTimeMillis() - time;
                                    time /= 60000;
                                    System.out.println("Step 3 Time: " + time + " minutes.");
                                    time = System.currentTimeMillis();
                                
                                    return;
                                }
                            }
                        }
                    }
                }
            }
            
            time = System.currentTimeMillis() - time;
            time /= 60000;
            System.out.println("Step 3 Time: " + time + " minutes.");
            time = System.currentTimeMillis();

            //Set of 5 primes is not found.  Increase search area.
            System.out.println("Increasing search area...");
            digitLimit++;
        }
    }
    
    private static boolean isPrime(long n){
        if(n % 2 == 0 || n % 5 == 0) return false;
        for(int i = 0; primesList.get(i) <= Math.sqrt(n); i++){
            if(n % primesList.get(i) == 0) return false;
        }
        return true;
    }
    
}

Okay, so after using Stereo's suggestion (nothing tricky with duplicate primes >_>), and meticulously testing each step of my new v3.0 algorithm, I have the results:

Output:

Code:

Step 1 Time: 2.1666666666666666E-4 minutes.
Step 2 Time: 0.38053333333333333 minutes.
[prime 1]
[prime 2]
[prime 3]
[prime 4]
[prime 5]
Sum: [sum]
Step 3 Time: 7.5E-4 minutes.

That's definitely an execution time of less than a minute =D Fitting a check to ensure that the sum of the 5 primes is the lowest is trivial at this point, aside from the "OutOfMemoryException" caused by the large-ass boolean table.

Thanks a lot Stereo and Devil's Sunrise! I've learned quite a few things from this exercise.